We introduce and analyse numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the...

Using big financial data for the price dynamics of U.S. equities, we investigate the impact that market microstructure noise has on modeling volatility of the returns. Based on wavelet transforms (DWT and MODWT) for decomposing the systematic pattern and noise, we propose a new wavelet-based...